Foundations of Math 11
Chapter 8 – Proportional Reasoning
Notes Booklet
Homework Assignments
(Nelson Foundations of Mathematics 11 Workbook)
Chapter 8 Proportional Reasoning
Section Topic
8.1
8.2
8.3
8.4
8.5
8.6
Review
Comparing and Interpreting Rates
Solve Problems with Rates
Scale Diagrams
Scale Factor and 2-D Shapes
Similar Objects
Scale Factor and 3-D Objects
Assignment
P219: 1-14
P226: 1-4, 6, 8-9
P229: 1-11
P235: 1-5, 7, 10
P239: 1, 3-9
P243: 1-7
P246--249
FOM11
8.1 Comparing and Interpreting Rates
A rate can always be expressed using the word _____________.
Examples:
$15/hr
14m/s
7.8L/100km
$1.56/kg
75Cal/hr
5.5%
Comparing rates as fractions
Ex1
Thrifty’s has either a 3.78L jug of apple juice for $6.99 or a 1.5L jug of
apple juice for $2.99. What is the cost per litre for each jug? Which one is
the better deal?
Comparing rates on graphs
Ex2
Describe what is happening in the
three sections of the graph to the
right. Use slope to decide which
section represents the fastest rate.
What are the units for slope in this
story?
FOM11
8.2 Solving Problems That Involve Rates
Review from 8.1:
Unit price =
Ex1
A dozen bagels costs $3.49. Find the unit price.
Ex2
Determine the unit cost for a 8kg sack of carrots that costs $12.77
Using fractions / Cross-multiplication
Ex3
It takes Jason 1 h 45 min to mow a 1350 sq ft. lawn. How long should it
take him to mow a 2200 sq ft lawn?
Longer problems
Ex4
Alice owns a T-shirt shop. She is choosing between two suppliers. One is
in Canada and will sell 300 T-shirts for $1015. The second is in Mexico and sells
200 T-shirts for 7000 Pesos. The exchange rate is $1 Can = 13.46 Pesos. Which
supplier has the cheaper price per T-shirt?
FOM11
8.3 Scale Diagrams
A Scale Diagram is one that is proportional to the object is represents.
The “scale” of the diagram is similar to the rates from 8.1 and 8.2, except that the
units cancel out:
10cm
Height of enlargement

Height of original
4cm
Ways to write Scale Factor:
Reduction or Enlargement?
Using Scale Factor to find missing dimensions:
Ex1
Darren builds a 0.02 model of an F1 MacLaren.
Ex2
It is 32km from Victoria to Sidney. If a map of the area has a scale of
The model is 12cm long. How long is the car in meters?
1:250 000, how far is Sidney from Victoria on the map, in centimeters?
FOM11
8.4 Scale Factors and Areas of 2-D Shapes
Scale Factor only describes a comparison between LINEAR distances:
15
2
3
10
When we want to compare the AREAS of similar shapes, though…
Ex1
A triangle with an area of 7 cm2 is enlarged by a scale factor of 1.5. What
Ex2
If the following figure is reduced by a scale factor of ¼, what would be the
is the area of the enlarged triangle?
area of the reduced figure?
5
Ex3
Find the Scale Factor for this pair of similar shapes
B
A
Area = 14cm2
Area = 70cm2
FOM11
8.5 Similar Objects: Scale Models & Diagrams
Review:
Ex1
This toy dinosaur is made to a scale of 1:48. What would the length and
height of the dinosaur be in real life?
24cm
30cm
Ex2
The Insanely large Costco-size box of Rice Krispies is a similar shape to
the regular box, but enlarged by 170%. If a regular box uses 2.5 square
feet of cardboard, determine the area of cardboard needed for the Jumbo
box.
Ex3
A filing cabinet is 136cm tall, 48cm wide and 60cm deep.
A diagram of the top, front and side views of the cabinet is drawn which is
12cm by 4cm by 5cm. Is this a scale diagram?
FOM11
8.6 Scale Factors and 3-D Objects
Ex1
The giant watering can in Beacon Hill Park is 20ft tall. If the watering can
on which it was based is 18 inches tall, determine the scale factor. How
many times greater is the surface area of the giant can? How many times
greater is the volume?
Ex2
If you made a similar can to the one in Ex1 by doubling the dimensions,
Ex3
Size 4 soccer balls have a circumference of 66cm. Size 5 soccer balls
how many times larger would the volume of the new can be?
(the standard size) have a circumference of 71cm. What % more leather
is used to make the standard size? What percent more air does it
contain?